Previous studies analyzing the impact of payoffs' cardinality in cooperation dilemmas have concluded that the additional benefits of defecting against a cooperator (the greed dimension) are more salient than the additional costs of cooperating against a defector (the fear dimension). We conduct an experiment to show that when the costs of cooperation exceed its gains, this pattern is reversed. The larger impact of fear over greed on the likelihood to defect is robust to random rematching and to repeated matching, and is mostly driven by a relative rather than an absolute perception of the incentives to cooperate across different dilemmas.